arXiv subjects
Publications and source records attributed to D. A. Garanin.
We have studied direct and Raman processes of the decay of electron spin states in a quantum dot via radiation of phonons corresponding to elastic twists. Universal dependence of the spin relaxation rate on the strength and direction of the magnetic field has been obtained in terms of the electron gyromagnetic tensor and macroscopic elastic constants of the solid.
We study the Landau-Zener Problem for a decaying two-level-system described by a non-hermitean Hamiltonian, depending analytically on time. Use of a super-adiabatic basis allows to calculate the non-adiabatic transition probability P in the slow-sweep limit, without specifying the Hamiltonian explicitly. It is found that P consists of a ``dynamical'' and a ``geometrical'' factors. The former is determined by the complex adiabatic eigenvalues E_(t), only, whereas the latter solely requires the knowledge of α_(+-)(t), the ratio of the components of each of the adiabatic eigenstates. Both factors can be split into a universal one, depending only on the complex level crossing points, and a nonuniversal one, involving the full time dependence of E_(+-)(t). This general result is applied to the Akulin-Schleich model where the initial upper level is damped with damping constant $γ$. For analytic power-law sweeps we find that Stueckelberg oscillations of P exist for gamma smaller than a critical value gamma_c and disappear for gamma > gamma_c. A physical interpretation of this behavior will be presented by use of a damped harmonic oscillator.
Spin-phonon relaxation due to two-phonon processes of a spin cluster embedded in an elastic medium has been studied. For the case of uniaxial anisotropy, relaxation rates due to Raman processes and processes involving the emission of two phonons have been obtained. For a biaxial spin Hamiltonian, the rates of transitions between tunnel-split levels have been computed. By comparison with the rates of corresponding direct processes, we have established temperature ranges where the Raman mechanism dominates over the one-phonon decay mechanism.
We study phonon-induced relaxation of quantum states of a particle (e.g., electron or proton) in a rigid double-well potential in a solid. Relaxation rate due to Raman two-phonon processes have been computed. We show that in a two-state limit, symmetry arguments allow one to express these rates in terms of independently measurable parameters. In general, the two-phonon processes dominate relaxation at higher temperature. Due to parity effect in a biased two-state system, their rate can be controlled by the bias.
We stress that the so-called butterfly hysteresis curves observed in dynamical magnetization measurements on systems of low-spin magnetic molecules such as V-15 and V-6 are a signature of adiabatic Landau-Zener transitions rather than that of a phonon bottleneck. We investigate the magnetization dynamics analytically with the help of a simple relaxation theory in the basis of the adabatic energy levels of the spin 1/2, to a qualitative accordance with experimental observations. In particular, reversible behavior is found near zero field, the corresponding susceptibility being bounded by the equilibrium and adiabatic susceptibilities from below and above, respectively.
Interaction of the electron spin with local elastic twists due to transverse phonons has been studied. Universal dependence of the spin relaxation rate on the strength and direction of the magnetic field has been obtained in terms of the electron gyromagnetic tensor and macroscopic elastic constants of the solid. The theory contains no unknown parameters and it can be easily tested in experiment. At high magnetic field it provides parameter-free lower bound on the electron spin relaxation in quantum dots.
We consider relaxation of a rigid spin cluster in an elastic medium in the presence of the magnetic field. Universal simple expression for spin-phonon matrix elements due to local rotations of the lattice is derived. The equivalence of the lattice frame and the laboratory frame approaches is established. For spin Hamiltonians with strong uniaxial anisotropy the field dependence of the transition rates due to rotations is analytically calculated and its universality is demonstrated. The role of time reversal symmetry in spin-phonon transitions has been elucidated. The theory provides lower bound on the decoherence of any spin-based solid-state qubit.
Quantum dynamics of a two-state spin system in a rotating magnetic field has been studied. Analytical and numerical results for the transition probability have been obtained along the lines of the Landau-Zener-Stueckelberg theory. The effect of various kinds of noise on the evolution of the system has been analyzed.
The asymptotic staying probability P in the Landau-Zener effect with interaction is analytically investigated at fast sweep, epsilon = pi Delta^2/(2 hbar v) << 1. We have rigorously calculated the value of I_0 in the expansion P =~ 1 - epsilon + epsilon^2/2 + epsilon^2 I_0 for arbitrary couplings and relative resonance shifts of individual tunneling particles. The results essentially differ from those of the mean-field approximation. It is shown that strong long-range interactions such as dipole-dipole interaction (DDI) generate huge values of I_0 because flip of one particle strongly influences many others. However, in the presence of strong static disorder making resonance for individual particles shifted with respect to each other the influence of interactions is strongly reduced. In molecular magnets the main source of static disorder is the coupling to nuclear spins. Our calculations using the actual shape of the Fe-8 crystal studied in the the Landau-Zener experiments [Wernsdorfer et al, Europhys. Lett. 50, 552 (2000)] yield I_0 that is in a good agreement with the value extracted from the experimental data.
We present numerical and analytical results for the swiching times of magnetic nanoparticles with uniaxial anisotropy at elevated temperatures, including the vicinity of T_c. The consideration is based in the Landau-Lifshitz-Bloch equation that includes the relaxation of the magnetization magnitude M. The resulting switching times are shorter than those following from the naive Landau-Lifshitz equation due to (i) additional barrier lowering because of the reduction of M at the barrier and (ii) critical divergence of the damping parameters.
We investigate the potential energy surface of a phi^4 model with infinite range interactions. All stationary points can be uniquely characterized by three real numbers $α_+, alpha_0, alpha_- with alpha_+ + alpha_0 + alpha_- = 1, provided that the interaction strength mu is smaller than a critical value. The saddle index n_s is equal to alpha_0 and its distribution function has a maximum at n_s^max = 1/3. The density p(e) of stationary points with energy per particle e, as well as the Euler characteristic chi(e), are singular at a critical energy e_c(mu), if the external field H is zero. However, e_c(mu) \neq upsilon_c(mu), where upsilon_c(mu) is the mean potential energy per particle at the thermodynamic phase transition point T_c. This proves that previous claims that the topological and thermodynamic transition points coincide is not valid, in general. Both types of singularities disappear for H \neq 0. The average saddle index bar{n}_s as function of e decreases monotonically with e and vanishes at the ground state energy, only. In contrast, the saddle index n_s as function of the average energy bar{e}(n_s) is given by n_s(bar{e}) = 1+4bar{e} (for H=0) that vanishes at bar{e} = -1/4 > upsilon_0, the ground state energy.
We show that the argument of Yukalov and Yukalova that dipole-dipole interaction prevents a system of magnetic dipoles from exhibiting superradiance unless assisted by a resonator is incorrect.
Two antiferromagnetically coupled tunneling systems is a minimal model exhibiting the effect of quantum-mechanical phase in the Landau-Zener effect. It is shown that the averaged staying probability oscillates vs resonance shift between the two particles, as well as vs sweeping rate. Such a resonance shift can be produced in Mn-4 dimers by the gradient of the magnetic field.
The strongly damping-dependent nonlinear dynamical response of classical superparamagnets is investigated by means of an analytical approach. Using rigorous balance equations for the spin occupation numbers a simple approximate expression is derived for the nonlinear susceptibility. The results are in good agreement with those obtained from the exact (continued-fraction) solution of the Fokker-Planck equation. The formula obtained could be of assistance in the modelling of the experimental data and the determination of the damping coefficient in superparamagnets.
We show that the theory of spin-phonon processes in paramagnetic solids must take into account the coherent generation of phonons by the magnetic centers. This effect should drastically enhance spin-phonon rates in nanoscale paramagnets and in crystals of molecular nanomagnets.
We report experimental studies of crystals of Mn12 molecular magnetic clusters in pulsed magnetic fields with sweep rates up to 4x10^3 T/s. The steps in the magnetization curve are observed at fields that are shifted with respect to the resonant field values. The shift systematically increases as the rate of the field sweep goes up. These data are consistent with the theory of the collective dipolar relaxation in molecular magnets.
We investigate the influence of interaction between tunneling particles and disorder on their avoided-level-crossing transitions in the fast-sweep limit. Whereas the results confirm expectations based on the mean-field arguments that ferromagnetic/antiferromagnetic couplings suppress/enhance transitions, we found large deviations from the mean-field behavior for dipole-dipole interactions (DDI) in molecular magnets Mn-12 and Fe-8. For ideal crystals of the needle, spherical, and disc shapes DDI tends to enhance transitions. This tendency is inverted for the needle shape in the presence of even small disorder in the resonance fields of individual particles, however.
We present a review of recent advances in the study of many-body effects in magnetic nanoparticles. Considering classical spins on a lattice coupled by the exchange interaction in the presence of the bulk and surface anisotropy, we investigate the effects of finite size, free boundaries, and surface anisotropy on the average and local magnetization for zero and finite temperatures and magnetic fields. Superparamagnetism of magnetic particles necessitates introducing two different, induced and intrinsic, magnetizations. We check the validity of the much used relation between them within different theoretical models. We show that the competition between the exchange and surface anisotropy leads to spin canting dependent on the orientation of the average magnetization with respect to the crystallographic axes and thus to a second-order effective anisotropy of the particle. We have also investigated the switching mechanism of the magnetization upon varying the surface anisotropy constant. Some cases of more realistic particles are also dealt with.